Spatiotemporally complete condensation in a non-Poissonian exclusion process

TL;DR

This paper studies a non-Markovian exclusion process where infinite variance in waiting times leads to a real-space condensate involving all particles, revealing complex dynamics due to history-dependent interactions.

Contribution

It introduces a non-Poissonian exclusion process with a novel condensation phenomenon driven by infinite-variance waiting times, advancing understanding of non-Markovian stochastic systems.

Findings

Infinite-variance waiting times induce complete space-time condensates.

Condensate formation depends on microscopic dynamics after failed hops.

The process exhibits non-Markovian behavior affecting stability and onset.

Abstract

We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that coarse-graining the interactions between particles in complex systems generically leads to a stochastic process with a non-Markovian (history-dependent) character. We characterize a large family of one-dimensional hopping processes using a waiting-time distribution for individual particle hops. We find that when its variance is infinite, a real-space condensate forms that is complete in space (involves all particles) and time (exists at almost any given instant) in the thermodynamic limit. The mechanism for the onset and stability of the condensate are both rather subtle, and depends on the microscopic dynamics subsequent to a failed particle hop attempts.